Question

A block mass $(m=0.1kg)$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force $F$ in the vertically downward direction. The linear momentum of the block increases by $2$$kgm{s}^{-1}$ in $1s$ after the block starts from rest. Then:

(Given $g=10m{s}^{-2}$)

• A. The tension in the string is $F$
• B. The tension in the string is $3N$
• C. The work done by the tension on the block is $20J$ during this $1s$
• D. The work done against the force of gravity is $10J$

Answer 1

Answer: (A), (B), (D)

The tension in the string is $F$
The tension in the string is $3N$
The work done against the force of gravity is $10J$

From the free body diagram
$F-mg=2$
$\Rightarrow$ $F=2+mg=3N$
also, $a=\frac{unbalancedforce}{mass}=\frac{2}{0.1}=20m/s^2$
$\therefore$ $S=\frac{1}{2}a{t}^2=\frac{1}{2}\times 20\times 1=10m$
Hence, work done by tension
$F\times 10=3\times 10=30J$
So, work done against gravity
$=mg\times S=1\times 10=10J$